Phasing of chains, sprockets, and gears to provide enhanced noise vibration and harshness reduction

ABSTRACT

A method for reducing NVH in a vehicle having the steps of providing at least one repeating event, replicating at least one component, and delaying at least one equivalent part. The repeating event is a complete cycle, such that the repeating event ends when the cycle begins to repeat itself. The component is replicated at least one time so that at least one equivalent part is formed. The equivalent part is delayed with respect to the component by angularly positioning the equivalent part with respect to the component in a predetermined way, such that at least one harmonic in the NVH-spectra is reduced during the component&#39;s repeating event and the equivalent part&#39;s repeating event in operation.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional Application No.60/835,406, filed Aug. 3, 2006.

BACKGROUND OF THE INVENTION

Almost all vehicles utilize a transfer case, a transmission, or both, inwhich gears, sprockets, and chains are used along with various othercomponents to transfer torque in order to move the vehicle. For example,torque is applied to a first gear from a motor or other driving devicewhich is operably connected to a second gear. As the torque is appliedto the first gear, the first gear rotates and moves the second gear inorder to transfer the torque. The same principle is applied tosprockets, where a chain operably connects two sprockets. Again, torqueis transferred through the transfer case or transmission in order tomove the vehicle. Torque is applied to a first sprocket, and therotation of the first sprocket moves a chain which causes a secondsprocket to rotate and transfer the torque.

However, undesirable noise, vibration, or harshness (NVH) can beproduced by the components in the transmission or transfer case. The NVHis produced because of the constant contacting of the chain with thesprockets or the contact between the gears. The NVH is undesirablebecause it causes vibrations which reduce the efficiency and durabilityof components on the vehicle, and it produces noise and vibrations whichare felt by the vehicle's occupants. The vibrations produced by thecomponents can also cause other components to come loose or reduce thedurability of other components.

Therefore, it is desirable to develop a method for reducing NVH causedby the components when in use. It is desirable to develop a system thatutilizes the same (or similar to original) components so that the systemdoes not need to be reconfigured while maintaining the distribution offorces applied to the components during the use of the system.

SUMMARY OF THE INVENTION

The present invention relates to a method for reducing NVH in a vehicleproviding the steps of providing at least one repeating event,replicating at least one component that causes the repeating event tocreate at least one equivalent part, and delaying at least oneequivalent part with respect to the original component. The at least onerepeating event is a complete cycle, such that the repeating event endswhen the cycle begins to repeat itself. The at least one component isreplicated at least one time so that at least one equivalent part isformed. The at least one equivalent part is delayed with respect to thecomponent by a predetermined amount, such that at least one harmonic ina NVH-spectra is reduced during the component's repeating event and theequivalent part's repeating event.

NVH generated by any repeating event can be described in terms of“harmonics”. In theory, there are infinite harmonics starting from one.These harmonics occur at specific frequencies depending upon how fastthe events are repeating themselves. NVH at these harmonics (especiallylower harmonics) is of very high concern. Exactly which harmonics aremost dominant can be experimentally determined. This invention paves fora way to provide an inventive method to minimize some or all of theproblem harmonics in a NVH spectra.

Let F(t) be a periodic event with a period of repetition T, then:F(t)=F(t+δT); where δ is 1, 2, 3

By Fourier theorem,${F = {a_{0} + {\sum\limits_{n = 1}^{\infty}{a_{n}{\cos\left( {\omega_{n}t} \right)}}} + {b_{n}{\sin\left( {\omega_{n}t} \right)}}}};$where n is the harmonic, t is time,

T is the period of repetition, a_(n),b_(n), and a₀ are Fouriercoefficients, and $w_{n} = {n{\frac{2\quad\pi}{T}.}}$

Thus, the above equation shows that any repeating event F(t) can bedescribed as a linear combination of harmonics. The above equations arealso valid for all of the components that produce repeating events whilein operation. Unless otherwise stated, the word “harmonic(s)” meansharmonic(s) of the repeating event.

In every component of interest, a certain event would mark the start ofa repeating event. Depending upon the component geometry, the start ofthe event may or may not be arbitrarily chosen. Similarly, there wouldan event marking the end of the repeating event. The time it takes tocomplete a repeating event will be represented by T.

In an arrangement comprising of a component and m-1 equivalent partsmaking a total of m “like” or “geometrically similar” entities andproducing m repeating events while in action, ideally the phasing wouldbe done in a way such that the starts of repeating events for twoconsecutive entities are T/m apart and no two repeating events start atthe same time. Strictly speaking, the delaying should be such that thestarts of each of the m-1 events leads the start of one and only onerepeating event by T/m and no two repeating events start at the sametime. The instance where two consecutive entities are T/m apart is asub-case of this general statement. In this arrangement, the harmonicsthat are a multiple for m are unaffected while all the rest arecompletely annulled. The number T/m has been derived after solvingmathematical equations for the system. In general, the higher the m, thebetter (lower) the NVH response would be. It should be noted thatphasing of component and equivalent parts means delaying of the start ofthe repeating events of the component and equivalent parts.

There might be a practical limitation on how large m can be in a systemof m like entities. In general, phasing the two consecutive repeatingevents by T/m where no two events start at the same time is the bestarrangement. This type of phasing would henceforth be called as“symmetrical delaying”. Although symmetrical delaying is the best way toobtain desirable NVH solution, in some cases it may require too manyreplications to be made on the original component. The exact number ofreplications required depends upon the NVH problem being addressed.Hence, sometimes, it might be beneficial (depending upon the problem athand) to have delay values other than as governed by the “symmetricaldelaying” rule and obtain some sort of a “compromise” or “next to best”solution. This form of delaying that is not governed by the rule of“symmetrical delaying” will be referred to as “asymmetrical delaying”.Words phasing and delaying are interchangeably used in this document.

Further areas of applicability of the present invention will becomeapparent from the detailed description provided hereinafter. It shouldbe understood that the detailed description and specific examples, whileindicating the preferred embodiment of the invention, are intended forpurposes of illustration only and are not intended to limit the scope ofthe invention.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention will become more fully understood from thedetailed description and the accompanying drawings, wherein:

FIG. 1 is a flow chart of a method for delaying an equivalent part withrespect to a component in accordance to the present invention;

FIG. 2 is a side perspective view of a chain assembly having anequivalent part delayed with respect to a component in accordance withan embodiment of the present invention;

FIG. 3 is a schematic plan view of a sprocket assembly having anequivalent part delayed with respect to a component in accordance withan embodiment of the present invention;

FIG. 4 is a schematic plan view of a gear assembly having an equivalentpart delayed with respect to a component in accordance with anembodiment of the present invention;

FIG. 5 is a perspective view of a gear assembly having an equivalentpart delayed with respect to a component;

FIG. 6 is a perspective view of a gear assembly having a plurality ofequivalent parts delayed with respect to the component;

FIG. 7 is a chart of an envelope function for an assembly of onecomponent and one equivalent part where the component is replicated onceand the equivalent part is symmetrically delayed in operation inaccordance with the present invention. An envelope function for anassembly of a component and m-1 equivalent entities is such that when itis multiplied by the NVH response of only one component, it gives theresponse due to the m phased component and equivalent entities puttogether. This envelope function is plotted for the case of symmetricaldelaying when m=2. It can clearly be seen that at many locations on thegraph (odd harmonics), the response is annulled;

FIG. 8 is a line graph for a percentage of response of the originalcomponent at the first harmonic as a function of phasing error(deviation from T/2 delay) when one component and one phased equivalentpart (m=2) are used. On the x axis, ξ signifies$\frac{2\quad\pi\quad y}{T}{radians}\quad{or}\quad\frac{360{^\circ}\quad y}{T}$where y is the error in time delay from its ideal delay time;

FIG. 9 is a line graph depicting the effect of an uneven loaddistribution on a component and at least one delayed equivalent part(m=2) on the NVH when one component and one ideally phased (i.e. withT/2 delay) equivalent part are used. Here, λ=0 corresponds to equaldistribution of loads on component and the equivalent part, while λ=±1represents the case when either the original component or the equivalentpart takes all the load; and

FIG. 10 is a graph illustrating optimal delay angles for a component andan equivalent part (m=2). The objective for this exercise was tominimize the sum of first, second and third harmonics such that thefirst and second harmonics are α and β times more important than thethird respectively where α and β are positive numbers.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The following description of the preferred embodiment(s) is merelyexemplary in nature and is in no way intended to limit the invention,its application, or uses.

Referring to FIG. 1, a method for reducing NVH on a vehicle is generallyshown at 10. First, a repeating or periodic event is defined(identified) at decision box 12. The repeating event is defined by acomplete cycle, such that the repeating event ends when the cycle beginsto repeat itself. Thus, the repeating event is defined by one completionof a cycle that repeats itself. In a preferred embodiment, the torsionalforce transfer components are operating under steady state conditions. Acomponent operates in a steady state condition when the repeating eventoccurs at the same rate as the immediately proceeding repeating event.However, it should be appreciated that the components can operate inwhat appears to be non-steady state conditions, since a non-steady statecondition is eventually a steady state condition over a sufficientlylarge finite period of time.

At decision box 16 the component is replicated a predetermined number oftimes to form at least one equivalent part. How many replications needto be performed depends upon the NVH problem being addressed. Theequivalent part that is produced from the replication has substantiallythe same design and functions as the original component. One form ofreplication is to construct a component and then construct an equivalentcomponent. In some cases, a form of replication is to construct theoriginal component and then splice the component to create an equivalentcomponent. However, when the component has been spliced the componentand resulting equivalent part(s) are now a portion of the width of thecomponent in its original state. The component and the equivalentpart(s) may or may not be cast on the same block of material. Forexample, in FIGS. 5-6, the component and the equivalent part(s) are bothon the same block of material. However, this is not necessary and thecomponent and equivalent part(s) may exist independent of each other, atdifferent locations. The advantage of casting them on the same materialpiece is that it occupies less space and hence is more packagingfriendly.

After the equivalent part has been produced, the equivalent part isphased or delayed with respect to the component at decision box 18. Whenthe equivalent part is delayed, the equivalent part is delayed apredetermined amount with respect to the component. Therefore, the startof equivalent part's repeating event is moved or phased with respect tothe start of component's repeating event by a predetermined amount. Theexact values of the phasing angles depend upon the NVH problem beingaddressed.

At decision box 20, the delaying of the equivalent part(s) with respectto the component eliminates or reduces harmonic(s) of concern inNVH-spectra from the repeating event of the component and equivalentpart(s). Any repeating event manifests itself as a plurality ofharmonics in NVH spectra, where a harmonic is a sine wave with itsfrequency as an integer multiple of the frequency of the repeatingevent. Theoretically, the NVH produced by the repeating events can bedescribed as a predetermined linear combination of harmonics. Theelimination or reduction of the harmonic(s) eliminates or reduces theNVH produced by component alone. Theoretically, the “symmetrical delay”(using the T/m rule) of the equivalent part(s) with respect to thecomponent should completely eliminate the harmonics that are a multipleof m, and thus completely eliminate the NVH produced at those harmonics.However, due to tolerances of machined parts, the equivalent part(s) maynot be exactly symmetrically delayed, which results in the reductionrather than elimination of the aforesaid harmonics.

The harmonics that are eliminated or reduced from the repeating eventare based upon the phasing relationship between the component and theequivalent part(s). Preferably, at decision box 22 an approximatelyequal load is applied to both the component and the equivalent part(s).By applying approximately an equal load to the component and theequivalent part(s), the durability of the component and the equivalentpart(s) is increased with respect to a component and delayed equivalentpart(s) where the load is not equally distributed, since an excessiveamount of force is not applied to either the component or the equivalentpart(s). Equal loading to the component and equivalent part(s) createsthe best reduction or elimination of NVH for specific harmonics, asshown in FIG. 9.

Referring to an embodiment as shown in FIG. 2, the component can be achain assembly generally indicated at 23 having an endless chain 24fabricated by a combination of links 25. For the purpose of NVH, chain24 is typically fabricated from at least two types of links 25 thatslightly differ in their geometry. The different links 25 are arrangedin a predetermined set pattern to complete a full length chain 24. Therandom combination of links 25 will be maintained for any replacementchain. The random combination of links 25 is a development prior to thepresent invention. The chain 24 is endless because an arbitrarybeginning at a link or blue link 28 is connected to an end at anadjacent link 27. The beginning and end of the chain are arbitrarybecause any point of the endless chain 24 is the beginning and end ofthe repeating event as created by the rotation of the chain 24. Therepeating event completes when the component 24 pattern starts to repeatitself. This repeating event may be equal to, or shorter than, a periodof chain 24 rotation depending upon the pattern of links 25. However,for the reasons of simplicity and without the loss of generality, allfurther discussions assume the repeating event to be the same as thecomplete rotation of the chain 24. Thus, the repeating event is definedby a complete rotation of the chain 24 where the blue link 28 completesa full cycle and returns to its initial position. Typically, inapplication, with a chain 24 being used for example but not limited to,a transfer case, the period of repetition and period of rotationcoincide. As mentioned previously, the links 25 which form the chain 24are placed in a predetermined combination, such that the links 25 candiffer in shape, so long as every link 25 is connected to an adjacentlink 25 on both ends.

The second chain 30 is substantially the same as the original chain 24including the same combination of links 25. The combined widths of chain24 and chain 30 essentially equal the width of a chain (not shown) priorto the present invention. Second chain 30 is then delayed with respectto the chain 24 so that a secondary blue link 32 is moved apredetermined amount from the blue link 28. For example, when the priorchain is replicated once to create two chains 24 and chain 30, the bluelink of the second chain 30 is delayed by T/2 with respect to the bluelink of the chain 24, where T is the period of rotation of the chain 24.However, the prior chain can be replicated (divided) multiple times tocreate multiple second chains, and the delaying of the multiple chainsis dependent upon the number of times the chain is replicated (divided).A preferred placement of the multiple chains can be determined by therules of symmetrical delaying as explained in preceding portions of thisapplication. In other words, the chains can be phased such that any ofthe two consecutive chains are delayed by T/m and no two repeatingevents start at the same time. Here, m is sum of equivalent parts(chains) and T is the time period of rotation of any of the chains.Thus, the equivalent blue links 32 are preferably proportionally orsymmetrically placed with respect to the blue link 28. Symmetricaldelaying is the most preferred way of phasing the various equivalentparts however it may sometimes require too many replications of theoriginal component. For such cases, one may determine an “optimal delaynumber” that might differ from what's required by symmetrical delaying.

In operation, the chain assembly 23 is operably connected to a firstsprocket 34 and a second sprocket 36. Typically, the chains 24, 30 andsprockets 34, 36 can be used in a transmission or transfer case on amotorized vehicle, but it is within the scope of the present invention,that the method be used where it is desirable to reduce NVH or the like.The blue link 28 is defined by arbitrarily choosing a beginning and endpoint of the chain 24 as described above. Then the repeating event isdefined by a single rotation of the chain 24 so that the blue link 28returns to its original position. During the repeating event,undesirable NVH is produced by the chain 24 when it contacts the firstsprocket 34 and the second sprocket 36. Thus, the NVH is produced atcertain harmonics during the repeating event. The second chain 30 isdelayed so that the equivalent blue link 32 is delayed by T/2 from theblue link 28 where T is the period of rotation. Based upon the delayingrelationship of the chain 24 and second chain 30, predetermined (allodd, as m=2) harmonics are eliminated or reduced from the response whicheliminates or reduces the NVH produced by the chain 24 and secondarychain 30 when contacting the first sprocket 34 and second sprocket 36.

The number of harmonics reduced during the repeating event is directlyrelated to the number of chains utilized, and how the secondary chainsare subsequently delayed with respect to the first chain of theassembly. If the phasing or delaying relationship is based upon T/m rule(symmetrical delaying) then the harmonics that remain unaffected basedupon the delaying of the secondary chain 30 from the chain 24 aredetermined by the equation:λm; where λ=1,2,3 . . . and m=the total number of secondary chain(s) 30and the chain 24.

The remainder of the harmonics are eliminated or reduced.

However, it is very difficult and time consuming to symmetrically delay(i.e. by using the T/m rule) the equivalent blue links 32 from the bluelink 28. In addition, the sprockets 34, 36 may be delayed with respectto one another further making it difficult aftain the exact delayrequirement for the chains. If the phasing of the second chain 30 is notgoverned by “symmetrical delaying” relationships the harmonics thatwould otherwise be eliminated, are now only reduced. When a harmonic isnot completely eliminated, the NVH produced by a given chain in theassembly at that harmonic is only reduced rather than completelyeliminated.

Referring to FIG. 3, a second embodiment of the present invention isshown where the component can be a sprocket assembly generally indicatedat 123 having a sprocket 124. Similar to the description above, thesprocket 124 has a series of teeth 138, where the choice of beginning orstarting tooth 128 is arbitrary. Again, assuming all the teeth 138 areapproximately alike, a repeating event provides the arbitrary beginning128 completing a rotation of ${\frac{2\pi}{L}\quad{rad}};$where L is the number of teeth 138 on the sprocket 124. Here, the timetaken for sprocket 124 to 2fr travel an angular distance of$\frac{2\pi}{L}\quad{rad}$will be the time period (T) of the repeating event.

Then the sprocket 124 is replicated (divided) so that an equivalent partof secondary sprocket 130 is formed from the original sprocket 124.Again, the secondary sprocket 130 is substantially similar to thesprocket 124, but if the secondary sprocket 130 is spliced from thesprocket 124, the sprocket 124 and the secondary sprocket 130 arethinner than the original sprocket 124. The starting points of theperiodic event of the original sprocket 124 and secondary sprocket 130are T/m=T/2 apart (delayed) as m=2. Here, m is the number of sprockets124, 130.

In operation, the sprocket 124 and secondary sprocket(s) 130 areoperably connected to a chain. Typically, the sprocket 124, sprocket(s)130, and chain(s) are used in a transmission or transfer case in amotorized vehicle, but it is within the scope of the present invention,that the method is used where it is desirable to reduce NVH. As thesprocket 124 and secondary sprocket 130 rotate and contact the chain NVHis produced. By replicating the sprocket 124 and delaying the secondarysprocket 130, harmonics are eliminated or reduced which eliminates orreduces the NVH produced by the sprocket 124 and secondary sprocket 130.If the phasing or delaying relationship is based upon the T/m rule(symmetrical delaying) then the harmonics which are unaffected by thedelaying of the secondary sprocket(s) 130 are determined by theequation:λm; where λ=1,2,3 . . . and m is the sum of secondary sprockets 130 andsprocket 124.

All of the remaining harmonics are eliminated or reduced.

When the load applied to the sprocket 124 and the secondary sprocket 130are not equal, the uneven load distribution results in less than optimalNVH and durability performances. First, the durability of the overloadedsprocket 124 or overloaded secondary sprocket 130 is reduced whencompared to a sprocket 124 and secondary sprocket 130 with an evenlydistributed load because of the excess load in which the overloadedcomponent must support. Also, the amount of NVH eliminated or reduced byreducing or eliminating harmonics in the repeating event due to thedelaying of the secondary sprocket 130 with respect to the sprocket 124is negatively affected.

In reference to FIGS. 3 and 9, when the load applied to the sprocket 124and secondary sprocket 130 are not equal, an uneven load distributionresults. As shown in the line graph in FIG. 9, for the case ofsymmetrical delaying, when the load distribution between the sprocket124 and second sprocket 130 are equal the NVH at the harmonic is reducedis zero. However, when an uneven load distribution is applied betweenthe sprocket 124 and the second sprocket 130, the NVH at the harmonicwhich otherwise goes to zero, now has some NVH but it is still less NVHthan the amount produced at the harmonic if the second sprocket 130 wasnot phased from the sprocket 124. In FIG. 9, λ=0 corresponds to equaldistribution of loads on the sprocket 124 and second sprocket 130, whileλ=±1 represents when the sprockets 124 or second sprocket 130 takes theentire load. It should be appreciated that the above description of thefunction referenced sprockets as an explanation but the function isapplicable to all of the components described or the like.

In reference to FIGS. 4 and 5, the component can be a gear assemblygenerally indicated at 223 having a gear 224 that has teeth 238. Similarto the description above, the gear 224 rotates and has an arbitrarybeginning gear tooth 228. Thus, the repeating event of the gear 224 isdefined by the starting gear tooth 128 rotating $\frac{2\pi}{L}$where L is the number of teeth 238 on the gear 224. The time taken torotate an angular distance of $\frac{2\pi}{L}$is the time period (T) of repetition.

The gear 224 is replicated (divided) in order to create a second gear230 with teeth 241. The start of the periodic event of the second gear230 is delayed with respect to that of gear 224 in the same manner asthe sprocket 124 described above in order to eliminate or reduce problemharmonics of the repeating event. Thus, the secondary gear 230 has anarbitrary beginning tooth 232 that is delayed with respect to thestarting tooth 228 of the gear 224. The elimination or reduction of NVHby delaying the secondary gear 230 with respect to the gear 224 is basedupon the same equations as the sprocket 124 described above. Likewise,it is preferred to evenly distribute the loads applied to the gear 224and the secondary gear 230.

It should be appreciated that the above method is applicable fordelaying other torsional force transfer members components in order toreduce NVH, which when in operation produce a repeating event, and areused to transfer forces.

In reference to FIG. 6, the gear assembly 223 has gear 224 beingreplicated (divided) multiple times to produce multiple (two) secondarygears 230. Secondary gears 230 are “symmetrically delayed” with respectto the gear 224 as governed by the T/m rule. Here m is the number ofsecondary gears 230 and gear 224, and T is the time period of repetitionof gear 224. Gears 224 and 230 can be one solid or connected piece or aseries of separated gears on a common shaft (not shown).

More specifically, in FIG. 6, the gear 224 is replicated twice (m=3) sothat the arbitrary starting tooth 239, 241 on the gears 230 are located$\frac{1}{3}\frac{2\pi}{L}\quad{rad}\quad{and}\quad\frac{2}{3}\frac{2\pi}{L}\quad{rad}$(or delayed by $\left. {\frac{T}{3}\quad{and}\quad\frac{2T}{3}} \right)$away from the tooth 228 of gear 224. In the above example, all of theharmonics that are multiples of 3 (3, 6, 9 . . . ) are unaffected andthe remaining harmonics (1, 2, 4, 5 . . . ) are reduced or eliminated.In another embodiment (not shown), the gear 230 having the startingtooth 241 can juxtapose the other two gears of the gear assembly.

Referring to FIG. 7, the graph shows the elimination or reduction of NVHharmonics for a sprocket which has been replicated once with thesecondary sprocket 130 being 'symmetrically delayed“with respect to theoriginal gear 124 (m=2). An envelope function, when multiplied by theNVH response of the original component 124 alone, reproduces theresponse from the assembly of sprockets 124 and 130 with the delayingrelations. This envelope function is based upon the symmetrical delayingequation referenced above where the unaffected harmonics are determinedby the equation:λm, λ=1,2,3

In this example, m=2 since the sprocket was replicated once and thesecondary sprocket 130 is delayed with respect to the sprocket 124.Thus, for this case, all odd harmonics are eliminated or reduced. On thegraph, the envelope function has a range from 0-1, where 1 is the amountof NVH produced by the sprocket when a single sprocket is used duringoperation. Thus, any point on the graph which is below 1 impliesreduction of NVH when compared to an assembly where a single sprocket isused. Except for the harmonics which are integer multiples of m, thereis an NVH reduction at all the other harmonics. It should be appreciatedthat the above description of the envelope function referenced gears asan explanation and not limitation, and the envelope function isapplicable to the other components 24, 124, 224 or the like.

In reference to FIG. 8, the line graph represents the NVH produced at aharmonic with varying load sharing between the sprockets 124, 130 forthe case when m=2 and the sprocket 130 is symmetrically delayed withrespect to sprocket 124. λ=0 when the two sprockets 124, 130 share equalloads and λ=±1 when either one of the sprockets 124, 130 take all theload. It can be seen that the best NVH response is obtained for the casewhen the load sharing is equal between the two sprockets (λ=0). For asystem of a sprocket 124 and m-1 equivalent sprockets 130 where allequivalent sprockets are symmetrically delayed and the load distributionis equal among all of the sprockets, the harmonics that are notmultiples of m are eliminated. However, the responses at the harmonicsthat are multiples of m are not reduced and produce NVH equivalent to asystem where a single sprocket is used. It should be appreciated thatthe above description of the graph referenced sprockets as anexplanation and not limitation, and the function is applicable to othercomponents 24, 124, 224, or the like.

With respect to the descriptions above of the method for delaying thecomponents 24, 124, 224 and the equivalent parts 30, 130, 230, ifreduction of the second harmonic is desired, the component 24,124, 224needs to be replicated at least twice to produce at least two equivalentparts 30, 130, 230 so that m equals three (m=3). If m equals three, thenboth the first and second harmonics (among others) will be eliminated.However, making multiple replications is expensive and at times it maybe desirable to reduce the first and second harmonics as much aspossible without replicating the component 24, 124, 224 multiple timesand produce multiple equivalent parts 30, 130, 230. It is possible toreduce the NVH produced at the second harmonic even when m=2 if it isacceptable to compromise the performance at the first harmonic. Thus,the equivalent parts 30, 130, 230 are “asymmetrically delayed” withrespect to the component 24, 124, 224, which results in a reduction ofthe first harmonic and second harmonic, but does not completelyeliminate the first harmonic as if the equivalent parts 30,130, 230 weresymmetrically delayed by T/2.

It can be expensive to replicate or splice a component such as a chain,sprocket, or gear once and can be even more expensive to replicate thecomponent multiple times. Also, the durability of a component can bereduced the more times the component is spliced. If the symmetricdelaying relation is used (T/m rule), then the harmonics other thanthose that are integer multiple of m are completely eliminated and theharmonics that are integer multiple of m are completely unaffected. Analternative approach is to set up optimization cirterion, which reducesthe desired harmonics but does not completely eliminate all of theaffected harmonics. The advantage of the optimization approach is thatit can give a reasonably good solution with lesser number ofreplications of components (examples 30, 130, 230) than as mandated bysymmetrical delaying (T/m) rule. The disadvantage is that not all the mproblem harmonics will be annulled. The following equations are ageneral statement for optimization for determining the phasing of theequivalent parts 30, 130, 230 to reduce the desired harmonics where thecomponents chain, sprocket, or gears are replicated (divided) m-1 times.For such a system, the amplitude of a dynamic quantity (like force,displacement etc) can be represented by$R_{m,k}^{2} = {E_{k}^{2}\begin{bmatrix}{\left( {1 + {\cos\left( {2\quad\pi\quad k\frac{\quad t_{\quad 1}}{\quad T}} \right)} + \ldots + {\cos\left( {2\quad\pi\quad k\quad\frac{\quad t_{\quad{m\quad - \quad 1}}}{\quad T}} \right)}} \right)^{2} +} \\\left( {0\quad + \quad{\sin\left( {2\quad\pi\quad k\quad\frac{\quad t_{\quad 1}}{\quad T}} \right)}\quad + \quad\ldots\quad + \quad{\sin\left( {2\quad\pi\quad k\quad\frac{\quad t_{\quad{m\quad - \quad 1}}}{\quad T}} \right)}} \right)^{2}\end{bmatrix}}$ ${Or},{R_{m,k} = {E_{k}{\sqrt{\begin{bmatrix}{\left( {1 + {\cos\left( {2\quad\pi\quad k\frac{\quad t_{\quad 1}}{\quad T}} \right)} + \ldots + {\cos\left( {2\quad\pi\quad k\quad\frac{\quad t_{\quad{m\quad - \quad 1}}}{\quad T}} \right)}} \right)^{2} +} \\\left( {0\quad + \quad{\sin\left( {2\quad\pi\quad k\quad\frac{\quad t_{\quad 1}}{\quad T}} \right)}\quad + \quad\ldots\quad + \quad{\sin\left( {2\quad\pi\quad k\quad\frac{\quad t_{\quad{m\quad - \quad 1}}}{\quad T}} \right)}} \right)^{2}\end{bmatrix}}}}}$

Here, R_(m,k) is the amplitude of the k^(th) harmonic and m is the totalnumber of original sprocket (gears) and equivalent sprockets (gears).E_(k) will be equal to the amplitude if m=1 (i.e, with no phasing).t_(i) is the delay between the start of periodic event on i+1^(th)sprocket (gear tooth) and the start of periodic event on the first.Let's assume that the harmonics of interest are S, where,

S={set of all harmoics of concern}

Then the optimization problem can be stated as follows.

Minimize F(t₁,t₂,t₃,t₄, . . . , t_(m-1)) such that

F(t₁,t₂,t₃,t₄, . . . , t_(m-1))=R_(a)+R_(b)+R_(c)+R_(d)+ . . . +R_(i)

Here,

-   -   [abcd . . . i]εS

And t₁,t₂,t₃,t₄, . . . , t_(m-1) are the delays of interest.

In general, this optimization problem can be set-up for minimizing anynumber of harmonics (n) for components chains, sprockets, or gears withany number of equivalent parts 30, 130, 230 (m-1). As an example, ifthis method is used with one component 24, 124, 224 and one equivalentpart 30, 130, 230 and the objective is to minimize both the first andsecond harmonics, the ability to completely eliminate the first harmonicis lost, but the benefit of reducing the second harmonic, which wouldotherwise be unaffected while using a two sprocket system withsymmetrical delay, is gained. Therefore, depending on which harmonicsare to be reduced and how many replications can be made, the optimaldelaying time is determined. Such delaying times may result in delayingrelationships other than as governed by the symmetrical delayingrelation.

As mentioned previously, from a cost perspective many applications ofthe present invention are limited to one component 24,124, 224 and oneequivalent part 30, 130, 230. In an example, for a two sprocket system,it is desired to minimize the sum of amplitudes of first three harmonicssuch that the first and second harmonics are α and β times moreimportant than the third harmonic respectively. Notice that if threereplications were to be performed (m=4), the first three harmonics willall be annulled—an ideal solution. But assuming that we only want tomake one replication, the following procedure shows the “best” or“optimal” delay for the case when m=2. For the case of one component 24,124, 224 and one equivalent part 30, 130, 230, amplitude of any (k^(th))harmonic can be written as:${Amplitude}_{k} = {{2\quad{\cos\left( {\pi\quad k\frac{t}{T}} \right)}}}$

Here, t is the delay between the starts of the two repeating events.This equation has been obtained by simplifying the expressionspreviously reported in the report. Hence, the optimization problem maybe posed as minimization of function F(t) with respect to t, where,${F(t)} = {{{\alpha\quad{\cos\left( {\pi\frac{t}{T}} \right)}}} + {{\beta\quad{\cos\left( {2\quad\pi\frac{t}{T}} \right)}}} + {{\cos\left( {3\quad\pi\frac{t}{T}} \right)}}}$

While a closed form solution is hard to find, one can plot F(t) forvarious values of t,α,β can be made to determine where the minima isreached. FIG. 10 shows the values of t (delay times) where a minima isreached for various values of α, β.

It can be seen that for small values of α & β, the optimum t/T is ⅙. Forsmall values of a and large values of β, the optimum t/T is ¼. For largevalues of α, and small values of β the optimum t/T is invariably ½.

Some specific cases are being pointed out here.

When α=0 and β=0.5, the best delay is T/6.

When α=0 and β=3, the best delay is T/3.

When α=3 and β=0, the best delay is T/2.

In general, the delays symmetrical and asymmetrical can be effectiveplus or minus 10%.

The description of the invention is merely exemplary in nature and,thus, variations that do not depart from the gist of the invention areintended to be within the scope of the invention. Such variations arenot to be regarded as a departure from the spirit and scope of theinvention.

1. A method for reducing NVH comprising the steps of: providing at leastone component; providing at least one repeating event of said at leastone component, wherein said at least one repeating event is a completecycle of said at least one component, such that said at least onerepeating event ends when said cycle begins to repeat itself;replicating said at least one component, wherein said at least onecomponent is replicated at least one time so that at least oneequivalent part is formed, wherein said equivalent part has one saidrepeating event; and delaying said at least one equivalent part withsaid at least one component, wherein said at least one equivalent partis moved with respect to said at least one component by a predeterminedamount, such that at least one harmonic in a NVH-spectra is reducedduring said at least one component's repeating event and said at leastone equivalent part's said repeating event.
 2. The method for reducingNVH of claim 1, wherein said equivalent part has substantially the samedesign as said component and same function as said component.
 3. Themethod for reducing NVH claim 1, wherein when said equivalent part isdelayed with respect to said component, said repeating event of saidequivalent part is delayed with respect to said repeating event of saidcomponent.
 4. The method for reducing NVH of claim 1, wherein a loadexperienced by said equivalent part is approximately equal to a loadexperienced by the said component, except that said loads are displacedin time.
 5. The method for reducing NVH on a vehicle of claim 1, whereinsaid NVH is produced at said harmonic, and a reduction of said harmonicreduces said NVH during said repeating event that said harmonic wasreduced.
 6. The method for reducing NVH on a vehicle of claim 1 furthercomprising the step of said component and said equivalent part are in atleast one of a transfer case and a transmission.
 7. The method forreducing NVH on a vehicle of claim 1 further comprising the step of saidcomponent is at least one of a sprocket, a chain, and a gear.
 8. Themethod for reducing NVH on a vehicle of claim 7, wherein when saidcomponent is at least one of said sprocket or said gear, and saidequivalent part(s) is delayed symmetrically (using T/m rule) withrespect to said component, all said harmonics are reduced except forsaid harmonics that are multiples of the sum of said component and saidequivalent parts.
 9. The method for reducing NVH of claim 7, whereinwhen said component is a chain, and said equivalent part(s) is delayedsymmetrically (T/m rule) with respect to said component, all saidharmonics are reduced except for said harmonics that are multiples ofthe sum of said component and said equivalent parts.
 10. The method forreducing NVH of claim 1, wherein when said component is replicated onceto produce one said equivalent part, start of the periodic event of thesaid equivalent part is delayed by T/2 with respect to said repeatingevent of said component, such that all odd said harmonics areeliminated.
 11. The method for reducing NVH claim 10, wherein one saidequivalent part is delayed by a predetermined amount other than T/2 withrespect to said component, in order to at least partially reduce a firstharmonic and a second harmonic of said repeating event of said componentand said repeating event of said equivalent part.
 12. The method forreducing NVH of claim 1, wherein when said component is replicatedmultiple times to produce a plurality of said equivalent parts, saidequivalent parts are at least one of symmetrically delayed andasymmetrically delayed with respect to said component.
 13. A method forreducing NVH comprising the steps of: providing at least one componentbeing at least one of a sprocket and a gear; providing at least onerepeating event of said at least one component, wherein said at leastone repeating event is a complete cycle, such that said at least onerepeating event ends when said cycle begins to repeat itself;replicating said at least one component, wherein said at least onecomponent is replicated at least one time so that at least oneequivalent part is formed, wherein said equivalent part has one saidrepeating event and said equivalent part has substantially the samedesign and function as said at least one component; providing said atleast one component and said at least one equivalent part is in at leastone of a transfer case and a transmission; and delaying said at leastone equivalent part with said at least one component, wherein said atleast one equivalent part is moved with respect to said at least onecomponent by a predetermined amount, that at least one harmonic in aNVH-spectra is reduced during said at least one component's repeatingevent and said at least one equivalent part's said repeating event. 14.The method for reducing NVH of claim 13, wherein when said equivalentpart is moved with respect to said component, said repeating event ofsaid equivalent part is delayed with respect to said repeating event ofsaid component, such that a first load applied to said component isapproximately equal to a second load applied to said equivalent part.15. The method for reducing NVH of claim 13, wherein said NVH isproduced at said harmonic, and a reduction of said harmonic reduces saidNVH during said repeating event that said harmonic was reduced.
 16. Themethod for reducing NVH of claim 13, wherein said equivalent part isdelayed symmetrically with respect to said component, all said harmonicsthat are reduced except for said harmonics that are multiples of the sumof said component and said equivalent part.
 17. A method for reducingNVH comprising the steps of: providing at least one component being achain; providing at least one repeating event of said at least onecomponent, wherein said at least one repeating event is a completecycle, such that said at least one repeating event ends when said cyclebegins to repeat itself; replicating said at least one component,wherein said at least one component is replicated at least one time sothat at least one equivalent part is formed, wherein said equivalentpart has one said repeating event and said equivalent part hassubstantially the same design and function as said at least onecomponent; providing said at least one component and said at least oneequivalent part is in at least one of a transfer case and atransmission; and delaying said at least one equivalent part with saidat least one component, wherein said at least one equivalent part ismoved with respect to said at least one component by a predeterminedamount, such that at least one harmonic in a NVH-spectra is reducedduring said at least one component's repeating event and said at leastone equivalent part's said repeating event.
 18. The method for reducingNVH of claim 17, wherein when said equivalent part is moved with respectto said component, said repeating event of said equivalent part isaltered with respect to said repeating event of said component, suchthat a first load applied to said component is approximately equal to asecond load applied to said equivalent part.
 19. The method for reducingNVH of claim 17, wherein said NVH is produced at said harmonic, and areduction of said harmonic reduces said NVH during said repeating eventthat said harmonic was reduced.
 20. The method for reducing NVH of claim17, wherein when said equivalent part is delayed symmetrically withrespect to said component, all said harmonics are reduced except forsaid harmonics that are multiples at the sum of said component and saidequivalent part.
 21. A torsional force transfer member assemblycomprising: an m number of total sprockets or gears; and wherein saidsprockets or gears are angularly phased with respect to one another. 22.A sprocket assembly as described in claim 21, wherein said torsionalforce transfer members are phased by$\frac{T}{m} \pm \frac{0.1\quad T}{m}$ from one another.
 23. A sprocketassembly as described in claim 21 having two torsional force transfermembers, said torsional force transfer members being phased from oneanother, from one of a group of${\frac{T}{2} \pm \frac{0.1\quad T}{2}},{\frac{T}{4} \pm \frac{0.1\quad T}{4}},{\frac{T}{6} \pm \frac{0.1\quad T}{6}}$phase delays.
 24. A chain and sprocket arrangement comprising: an mnumber of chains; and and wherein said chains are angularly phased withrespect to each other.
 25. A chain and sprocket arrangement as describedin claim 27, wherein the chains are phased by$\frac{T}{m} \pm \frac{0.1\quad T}{m}$ from one another.